{"paper":{"title":"The cb-norm approximation of generalized skew derivations by elementary operators","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.OA","authors_text":"Ilja Gogi\\'c","submitted_at":"2019-06-13T08:40:19Z","abstract_excerpt":"Let $A$ be a ring and $\\sigma: A \\to A$ a ring endomorphism. A generalized skew (or $\\sigma$-)derivation of $A$ is an additive map $d: A \\to A$ for which there exists a map $\\delta:A \\to A$ such that $d(xy)=\\delta(x)y+\\sigma(x)d(y)$ for all $x,y \\in A$. If $A$ is a prime $C^*$-algebra and $\\sigma$ is surjective, we determine the structure of generalized $\\sigma$-derivations of $A$ that belong to the cb-norm closure of elementary operators $\\mathcal{E}\\ell(A)$ on $A$; all such maps are of the form $d(x)=bx+axc$ for suitable elements $a,b,c$ of the multiplier algebra $M(A)$. As a consequence, if"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1906.05548","kind":"arxiv","version":3},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}